Find the square roots of the following: `i`

Answer

`sqrt(i) = pm 1/sqrt(2) (1+i)`

Explanation

Let `sqrt(i)​=x+iy`.

Then `i=x^2-y^2+2ixy`,

`therefore` `x^2-y^2=0` and `2xy=1`.

Solving these, we get `x=y=pm 1/sqrt(2)`​.

Thus,

`sqrt(i) = pm(1/sqrt(2) + 1/sqrt(2) i) = pm 1/sqrt(2) (1+i)`